A rectangular prism with a volume of 3x^3+16x^2+5x cubic units has a base area of x^2+5xsquare units. Find the height of the rectangular prism.

Answer: No this is not a linear function as the y values have different first differences.

Step-by-step explanation:

First we look at the x values. We start off and look at the second x value and subtract the first x value from it (That would be 1-0) and that equals to 1. Then we look at the third x value and subtract the second x value from it (2-1) and that equals to 1. Then we look at the fourth x value and subtract the third x value from it (That would be 3-2) and that is 1. Next we look at the fifth x value and subtract the fourth x value from it (That would be 4-3) and that is 1.

Now we look at the y values and do the same thing as with the x values. We start off and look at the second y value and subtract the first y value from it (That would be 1-0) and that equals to 1. Then we look at the third y value and subtract the second y value from it (4-1) and that equals to 3. Then we look at the fourth y value and subtract the third y value from it (That would be 9-4) and that is 5. Next we look at the fifth y value and subtract the fourth y value from it (That would be 16-9) and that is 7.

Even though the x values all have the same first differences, the y values do not and so this cannot be a linear function.

I hope this helps. Tell me if something doesn't make sense.

Answer:

No, it is a quadratic relation.

Step-by-step explanation:

Work out the first differences between the given y-values:

[tex]0 \underset{+1}{\longrightarrow} 1 \underset{+3}{\longrightarrow} 4 \underset{+5}{\longrightarrow} 9 \underset{+7}{\longrightarrow} 16[/tex]

As the first differences are not the same, this is not a linear relation.

Work out the second differences:

[tex]1 \underset{+2}{\longrightarrow} 3\underset{+2}{\longrightarrow}5\underset{+2}{\longrightarrow}7[/tex]

As the second differences are the same, the relation is quadratic and will contain an x² term. The coefficient of x² is always half of the second difference.  As the second difference is 2, the coefficient of x² is one.

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x & 0 & 1 & 2 & 3 & 4\\\cline{1-6}x^2 & 0 & 1 & 4 & 9 & 16\\\cline{1-6}\end{array}[/tex]

Comparing x² with the given y-values, we can see that no further operation is needed.  Therefore, the relation is quadratic and the equation is [tex]y=x^2[/tex].

The sum of the length of the overall pattern in the given cartesian coordinate is calculated as; 44

We are told that The final line on the plan is parallel to the y-axis and passes through x = -10

Now, looking at the pattern, the lengths of each side are as follows;

1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5

Thus, the sum of the length of the overall pattern is calculated as;

1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 + 6.5 = 44

Therefore we can conclude from all the deductions and calculations above that the sum of the length of the overall pattern in the given cartesian coordinate is calculated to be; 44

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[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\\[/tex]

The [tex]\mathrm{distributive \: property}[/tex] states that an expression that is given in the form of [tex]\small\sf{ A(B + C)}[/tex] can be solved as [tex]\small\sf{A \times (B + C) = AB + AC}[/tex] . So:

[tex]\small\longrightarrow\sf{-24-18-2+4}[/tex]

[tex]\small\longrightarrow\sf{-42+2}[/tex]

▪ [tex]\large\tt{All \: \: options \: \: are \: \: wrong}[/tex]

[tex]\\[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\small\longrightarrow\sf{−6 (2^2+3) − 2 (1^2 - 2) = \underline{-6(4+3)}}[/tex]

Answer:

y = 1/5x -3

Step-by-step explanation:

Use y = mx +b as your model.  We plug in our slope for me and our y-intercept for b.

With the aid of the attached diagrams in the question, we have;

1- Linear relation

2- W = 8•P + 80

3- Please find attached the graph created using a graphing calculator.

4- a) The initial value is the mass of the vase

b) The slope is the mass of each pebble

5- The initial value is lesser than 80

6- 1.2 kilograms

7- 53 pebbles

8- a)

b) (0, 80)

c) The masses are the same

9- Trapezoid area, A = 14•x² - 4•x

10- Tanya and Leah are 18 and 6 years old respectively

1- The relationship between two variables (x and y) is linear if the difference between the terms of the x-values and the terms of the y-values are both constant.

From the table we have;

The relationship between the x and y-values in the table is therefore;

2. The slope, m, of the linear function is found as follows;

m = (360 - 280)/(30 - 20) = 8

The equation is therefore;

W - 360 = 8•(P - 30)

W = 8•P - 240 + 360 = 8•P + 80

3. Please find attached the graph drawn with a graphing calculator.

4. The initial value is the output variable (W-value) when the input variable (P-value) is zero.

Therefore;

y = 8×0 + 80 = 80

a) The initial value indicates when the input, P-value is zero, which gives the mass of the vases

b) The slope indicates the number of times an additional pebble increases the weight of the vase and pebble, which is the mass of one pebble

5- A styrofoam cup is lighter than a glass cup, therefore, the initial value, which is the constant term, c, reduces.

6- The weight, W, of 112 pebbles is therefore;

W = 10 × 112 + 80 = 1,200

7- 504 = 8•P + 80

Which gives;

504 - 80 = 8•P

P = 424 ÷ 8 = 53

8- Wilma's equation is; W = 10•P + 80

a) Please find the second graph showing the graphs of the two equations combined.

b) The point of intersection is given by the relation 10•P + 80 = 8•P + 80

2•P = 0

P = 0

Therefore, at the point of intersection, W = 80

The coordinates of the point of intersection is therefore;

c) The point of intersection means that the weight of Wilma's vase and the vase in question 1 are the same.

9. The area of the trapezoid, A, can be expressed as follows;

A = 4•x × ((2•x + 5)+(5•x - 7))/2

A = 2•x × (7•x - 2) = 14•x² - 4•x

10. Let T represent Tanya's age now and let L represent Leah's current age, we have;

T = L + 12

T - 3 = (L - 3) × 5

Solving gives;

L + 12 - 3 = (L - 3) × 5 (Substitution property)

L + 9 = 5•L - 15

4•L = 9 + 15 = 24

L = 24 ÷ 4 = 6

T = L + 12

Therefore;

T = 6 + 12 = 18

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Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.

Formular for the area of a kite is expressed as;

A = pq/2

Where p and q are the two diagonals of the kite.

Given the data in the question;

From the diagram, we can determine line AM and line MD using Pythagoras theorem.

c² = a² + b²

First, we find line AM

c² = a² + b²

5² = 3² + b²

25 = 9 + b²

b² = 25 - 9

b² = 16

b = √16

b = 4

Line AM = 4

Next, we determine Line MD

c² = a² + b²

(√58)² = 3² + b²

58 = 9 = b²

b² = 58 - 9

b² = 49

b = √49

b = 7

Line MD = 7

Now, we can find the area of the kite.

Diagonal p = BC = 6

Diagonal q = AD = AM + MD = 4 + 7 = 11

Area = pq/2

Area = [ 6 × 11 ]/2

Area = 66 / 2

Area = 33cm²

Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.

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Amount of money earned per number of hours of work =  [tex]f(g(x)) = 6x^{3} + 4[/tex]

To evaluate a composite function f(g(x)) at some x = a, first compute g(a) by substituting x = a in the function g(x). Then substitute g(a) into the function f(x) by substituting x = g(a). In the same way, we can calculate g(f(a)) as well.

Required calculation -

Amount of money (the earning) per unit x = [tex]f(x) = 2x^{2} + 4[/tex]

Number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works = [tex]g(x) = \sqrt{3x^{3}}[/tex]

we are to find the composite function [tex]f(g(x))[/tex]

Substituting g(x) into the x of f(x), we find:

[tex]f(g(x)) = 2(\sqrt{3x^{3} } )^{2} + 4\\\\= 2(3x^{3} ) + 4\\= 6 x^{3} + 4[/tex]

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Answer:

f(g(x)) = 6x3 + 4 dollars over hour

Step-by-step explanation:

Answer:

y = 2x - 11.

Step-by-step explanation:

Use the point-slope form of the straight line.

y - y1 = m(x - x1)   where m = slope and (x1, y1) is the given point.

Here m = 2 and (x1, y1) = (7,3) so the equation is:

y - 3 = 2(x - 7)

y - 3 = 2x - 14

y = 2x - 11

Answer:

a) Class A has the larger interquartile range.

b) Class A has the highest test score.

c) Class B has higher median test score.

d) Class B has smaller range of test score.

Step-by-step explanation:

a) Inter quartile range (IQR) =  upper quartile - lower quartile

  Class A:  IQR = 79 - 65 = 14

  Class B: IQR = 77 - 70 = 7

Class A has larger interquartile range.

b)  Class A has the highest test score.

c) Median of class A = 70

 Median of class B   = 74

Class B has higher median test score.

d) Range is the difference between the highest and lowest score.

Range = highest score - lowest score

 Range of Class A = 85 - 62 = 23

 Range of class B  =  79 - 68 = 11

Class B has smaller range of test score.

Answer:

$9600 saving / year

Step-by-step explanation:

1/5 of $21000 = 21000 / 5 = $4200 / month on rent

3/7 of $21000 = (21000 / 7) x 3 = $9000 / month on food (shocking right :) food is expensive)

1/3 of $21000 = 21000 / 3 = $7000 on other expenses / month

total savings/month = salary/month - rent/month - food/month - other expenses/month

total savings/month = 21000 - 4200 - 9000 - 7000

total savings/month = $800

BUT the question asks for savings per year. therefore, we must multiply the savings per month by total months per year (12)

800 x 12 = $9600

the person's total savings per year, with a salary of $21000 per month, is equal to $9600 per year

Answer:

Here is the full list of equivalent fractions to 32.  3/2, 6/4, 96, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40

Step-by-step explanation:

hope this helped you please add brainliest :)

Answer:

(15,0) , (0,6)

Step-by-step explanation:

Same concept as the previous 2 questions.

x-intercept is where the line touches the x-axis, and y = 0.

when y = 0,

12x + 30(0) = 180

12x = 180

x = [tex]\frac{180}{12}[/tex]

x = 15

Therefore the coordinates of the x-intercept is (15,0)

y-intercept is where the line touches the y-axis, and x = 0.

when x = 0,

12(0) + 30y = 180

30y = 180

y = [tex]\frac{180}{30}[/tex]

y = 6

Therefore the coordinates of the y-intercept is (0,6)

The area of the polygon is 25.5 square units

From the figure, we have the following coordinates

A = (-2, 1)

B = (3, 2)

C = (5, -3)

D = (-1, -3)

The area of the polygon is then calculated as:

A = 0.5 * |(x1y2 - x2y1) + (x2y3 - x3y2) + (x3y4 - x4y3) + (x4y1 - x1y4)|

Substitute the known values in the above equation

Area = 0.5 * |(-2 * 2 - 3 * 1) + (3 * -3  - 5 * 2) + (5 * -3  + 1 * -3) + (-1 * 1 + 2 * -3)|

Evaluate the sum of products

Area = 0.5 * |-51|

Remove the absolute bracket

Area = 0.5 * 51

Evaluate the product

Area = 25.5

Hence, the area of the polygon is 25.5 square units

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The function that best models the position of the weight is s(t) = 6cos (pi/2*t).

From the information, we know that the spring is going to have a sin or a cos equation.

We have that the maximum distance of the spring is 6 inches and it is achieved at t=0. We have that the function is of the form 6sin(at+B).

We have that the period is 4 minutes and therefore that the time component in the equation needs to make a period (2pi) in 4 minutes.

In general, a=2pi/T where a is this coefficient, T is the period. Finally, for B, since sin(pi/2)=1, we have that B=pi/2 because when t=0, we have that 6sin(B)=6.

Substituting, we have s(t) = 6cos (pi/2*t).

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Answer:

6pi

Step-by-step explanation:

First, find the circumference of the circle with radius 9. The formula is C = 2*pi*r, so C = 2*pi*9 = 18pi. Since arc is intercepted by the 120 degree central angle, the arc length is essentially 120/360 = 1/3 of the circumference. So, the arc length is 18pi*1/3 = 6pi, or approximately 18.850.

Answer:

50 days

Step-by-step explanation:

40×300=1200

1200-700

500

so 1 day is 10 . 50 days is 500

The number of days he was absent from work will be 50 days

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a man gets Rs. 40 for every day he works, but is fined Rs. 10 for every day he is absent If he got Rs. 700 at the end of 30 days.

The number of days he was absent from work will be calculated as below:-

40×300 = 1200

             = 1200-700

             = 500

1 day is 10 then 50 days is 500. Therefore, the number of days he was absent from work will be 50 days

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The property best describes the Function f IP 4- to- 1 Correspondance.

f is Nat Bijective since Not one-one.

x1= 010101 = 010111

then 2 and 7 2 maps to 0101

So f is mat one-one.

fip Mat 2 - to- 1 correspondance

Since

2 , = 0101 vo , 212 = 0101 01 , 23 = 010 / 1 1

One point 0101

go,

f is Not 2 - to- 1 correspondance.

7 12) is the storing a with the last two

bits mold so we have only $ possibility

of 4 strings going to a single storing.

f can not be 16 - to - 1 correspondance.

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Answer:

Step-by-step explanation:

Just multiply how much she waxes in 3/5 hour by 5/3.  Answer is 100/3 or 33.33 sq. meters per hour

the vertex of the function g(x) = f(x 2) .

If a quadratic equation is expressed as the following

                          [tex]y=a(x-h)^{2}+k[/tex]

It is then said to be in vertex form. Because the vertex point (peak point) occurs on the graph of this equation, it is so named (h,k)

The parabola that the quadratic equation depicts has this point (h,k) as its vertex.

We first remove the x squared coefficient, and then inside the bracket, we strive to create a condition that resembles a perfect square.

So, this is what we have:

                         [tex]$f(x)=x^{2}+6 x+3$\\$g(x)=f(x-2)$[/tex]

Thus, we obtain:

                        [tex]\begin{aligned}&g(x)=f(x-2) \\&g(x)=(x-2)^{2}+6(x-2)+3 \\&g(x)=x^{2}-4 x+4+6 x-12+3 \\&g(x)=x^{2}+2 x-5\end{aligned}[/tex]

Vertex form transformation of g(x):

                             [tex]\begin{aligned}&g(x)=x^{2}+2 x-5 \\&g(x)=x^{2}+2 x+1-1-5 \\&g(x)=(x+1)^{2}-9 \\&g(x)=(x-(-1))^{2}-6 \\&g(x)=(x-(-1))^{2}+(-6)\end{aligned}[/tex]

By comparing this[tex]a(x-h)^{2}+k[/tex] to, we obtain the coordinates of the vertex of the graph of g(x) as (h,k) = (-1,-6), as shown below.

As a result, the vertex of the function g(x) = f(x 2) .

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Answer:

question no c 0•08

Step-by-step explanation:

at first

1/4+1/3-1/2

0•25+0.33-0.50

0.58-0.50

0.08 answer

The function  which represents the modified design of the roller coaster is Y = 2f(0.15x²-10x+C).

What  define a function?

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here, the function: Y = 2f(0.3x - 1) + 10

Therefore, to transform the function

We have to compare with a general function and integrate.

g(x) = f(bx + c).

We now integrate to transform the function which gives us

Y = (2f) integral {0.3x - 1} + 10

Y = 2f { 0.15x² - x } + 10x + c

Y = 2f(0.15x²-10x+C)

Modified design of roller coaster is

Y = 2f(0.15x²-10x+C)

Thus, the function  which represents the modified design of the roller coaster is Y = 2f(0.15x²-10x+C).

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Answer:

A graph 1

Step-by-step explanation:

Answer: y=-3m+13

Step-by-step explanation:

y=mx+c

m is the gradient

y=-3x+c

We know one point

-2=3(-5)+c

Solve for c

-2=-15+c

13=c

y=-3m+13

Answer:

A, C, D

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

1) Based on the given conditions, formulate:

30 meters/100 meters

2) Calculate 30 meters/100 meters:

3/10

3) Convert to percentage:

- 3/10 x 10/10

- 3x10/10x10

30/100

30/100 = 30%

You’re done!

Also, if you could label this brainliest that would be a great help!

Thanks xx

-Dante

First you have to figure out the side length of the triangle.

sin(60)= X/8

Let's call x the side length.

8 sin(60)=X

X=6.93

The multiply it by 4

The area is 27.72

There are 30240 ways in which we can select five people from a group of ten if the order of selection is important.

Given that there are 10 total number of people.

We are required to find the number of ways in which 5 people can be selected from 10 people.

Permutations is basically the number of arrangements that can be possible with the number of things , people, etc. It is denoted as [tex]nP_{r}[/tex]=n!/(n-r)!.

We have 10 people and we have to select 5 people from them then the number of ways can be find out by [tex]10P_{5}[/tex].

We have to expand this permutation.

=10!/(10-5)!

=10!/5!

=10*9*8*7*6*5!/5!

=10*9*8*7*6

=30240 ways

Hence there are 30240 ways in which we can select five people from a group of ten if the order of selection is important.

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The function can be solved as follows:

(h - g)(2.1) = 3.51

g(x) = 2x² + 3x - 9

h(x) = x² + 2x - 6

(h - g)(x) = h(x) - g(x)

(h - g)(x) = 2x² + 3x - 9 - ( x² + 2x - 6)

(h - g)(x) =  2x² + 3x - 9 - x² - 2x + 6

(h - g)(x) = 2x² - x² + 3x - 2x - 9 + 6

(h - g)(x) = x² + x - 3

Therefore,

(h - g)(2.1) = (2.1)² + (2.1) - 3

(h - g)(2.1) = 4.41 + 2.1 - 3

(h - g)(2.1) = 6.51 - 3

(h - g)(2.1) = 3.51

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Answer:

rotate 180° about origin

The preimage and image of the figure are given below. The transformation rule that is applied is (x, y) → (-x, y).

Given a triangle with vertices A(—3, 2), B(—l, —l), and C(—4, —2), which is preimage. Further, an image is created of this triangle that has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). As shown in the given figure.

Now, as per the image and preimage in the given graph. The image is the reflection of the preimage about the y-axis. This can be verified as when the image and preimage are reflected about the y-axis the vertices change as:

(x, y) → (-x, y)

A(-3, 2) → A'(3,2)

B(-1, -1) → B'(1, -1)

C(-4, -2) → C'(4,-2)

Hence, the transformation rule is (x, y) → (-x, y).

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Answer: 88°

Step-by-step explanation:

We know that the ratio of ∠DCB : ∠ACD is 3:1. In other words, ∠DCB is [tex]\frac{3}{3+1}[/tex], or [tex]\frac{3}{4}[/tex] of the whole angle (i.e., ∠ACB), while ∠ACD is [tex]\frac{1}{4}[/tex] of the whole angle.

To easily find ∠ACB, which is the sum of both angles, we can add up all the angles of [tex]\triangle ABC[/tex] and set it equal to 180°.

[tex]m\angle A + m\angle B + m\angle ACB = 180\\75+53+m\angle ACB=180\\128+m\angle ACB=180\\m\angle ACB=52[/tex]

From here, we can calculate ∠BCD by multiplying the value of ∠ACB by three-fourths.

[tex]m\angle BCD = \frac{3}{4}(m\angle ACB)\\m\angle BCD = \frac{3}{4}(52)\\m\angle BCD = 39[/tex]

Similar to what we did to get the measure of ∠ACB, we can add up all the angles measures of [tex]\triangle DBC[/tex] to get the measure of ∠BDC.

[tex]m\angle B + m\angle BDC + m\angle BCD = 180\\53+m\angle BDC + 39= 180\\92+ m\angle BDC=180\\m\angle BDC = 88[/tex]

The measure of ∠BDC is 88°.